Closure of VP under taking factors: a short and simple proof

03/06/2019
by   Chi-Ning Chou, et al.
0

In this note, we give a short, simple and almost completely self contained proof of a classical result of Kaltofen [Kal86, Kal87, Kal89] which shows that if an n variate degree d polynomial f can be computed by an arithmetic circuit of size s, then each of its factors can be computed by an arithmetic circuit of size at most poly(s, n, d). However, unlike Kaltofen's argument, our proof does not directly give an efficient algorithm for computing the circuits for the factors of f.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset